Answer:
a) K = 2/3 π G m ρ R₁³ / R₂
, b) U = - G m M / r
Explanation:
The law of universal gravitation is
F = G m M / r²
Part A
Let's use Newton's second law
F = m a
The acceleration is centripetal
a = v² / R₂
G m M / R₂² = m v² / R₂
v² = G M / R₂
They give us the density of the planet
ρ = M / V
V = 4/3 π R₁³
M = ρ V
M = ρ 4/3 π R₁³
v² = 4/3 π G ρ R₁³ / R₂
K = ½ m v²
K = ½ m (4/3 π G ρ R₁³ / R₂)
K = 2/3 π G m ρ R₁³ / R₂
Part B
Potential energy and strength are related
F = - dU / dr
∫ dU = - ∫ F. dr
The force was directed towards the center and the vector r outwards therefore there is an angle of 180º between the two cos 180 = -1
U- U₀ = G m M ∫ dr / r²
U - U₀ = G m M (- r⁻¹)
We evaluate for
U - U₀ = -G m M (1 /
- 1 /
)
They indicate that for ri = ∞ U₀ = 0
U = - G m M / r
Answer:
Explanation:
Work done in carrying bricks
mgh
= 207 x 9.8 x 3.65
-= 7404.4 J
Work done in compressing gas
PΔV
Pressure x change in volume
1.8 x 10⁶ ΔV = 7404.4
ΔV = 7404.4 / 1.8 x 10⁶m³
= 4113.33 x 10⁻⁶ m³
= 4113.33 cc
Answer:
Final velocity, V = 11.5m/s
Explanation:
Given the following data;
Initial velocity, U = 2.5m/s
Acceleration, a = 1.5m/s²
Time, t = 6secs
To find the final velocity, we would use the first equation of motion
V = U + at
Substituting into the equation, we have
V = 2.5 + 1.5*6
V = 2.5 + 9
Final velocity, V = 11.5m/s